# Homework Help: Magnetization and Spins

1. Jan 3, 2008

### touqra

Consider the degenerate electron gas in a metal as a mixture of two gases of spin-up and
spin-down electrons, respectively. when a small magnetic field B is applies, a few of the
electrons reverse their spins so as to maintain equality of the chemical potential in the two
mixed gases. For T = 0, find the magnetic susceptibility of the metal $$( \frac{\partial M}{\partial B} )_N_,_V$$ ,
where M is the magnetization (magnetic moment per unit volume), N is the total number of electrons, and V is the volume. The magnetic moment of the electron is μB.

How do I use the information of chemical potential equality to solve this problem? I am thinking that since Gibbs, $$G_{up} = \mu n_{up}$$ and the same for spin down gas, the change, $$dG = \mu dn + n d \mu = \mu dn$$. What next ?

Last edited: Jan 3, 2008